Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

POSTULATE PROPERTIES 119
which a collection of such functions has an ambiguous,
or undetermined, subject-matter that may or may not
be compendent? May I leave this subtle matter to your
reflection?
As to compatibility, suppose we have a collection of
functions such that we have not been able either to
verify them or to prove them incompatible. Doubtless,
we must say, in such a case, that we do not know whether
the collection is compatible or not. Might not the collection be incompatible without our being able ever to
discover the fact? Might it not be compatible, though
we should never be able to know it? Another questionvery different from the preceding one-is this: Is there,
conceivably, a compatible or a not incompatible collection
of propositional functions having no verifiers in our
world?
What, essentially, is logical compatibility? Must we
be content with mere examples of it or with what seems
at all events to be such examples? Whatever logical
compatibility may be, it evidently is such that compatibility and incompatibility are related somewhat as
pleasure and pain, as cosmos and chaos, as music and
noise, as health and disease, as harmony and discord,
as beauty and ugliness-so that Logic and Science are no
less under the empire of the muses than are the Arts.
Is compatibility, then, an emotion, a feeling, a mere
sentiment? If it be, it is not one of ideas, but is a sentiment of forms-propositional forms. What is propositional form? The question arose before and I said we
should return to it. Well, here it is. I can not answer
it. I know, in a sense, and so do you, what such form
is, but I cannot define it abstractly,-not satisfactorily.
Possibly you can-sometime; and if you do, you will